C-THERM TCi, Operator'S Manual, Page: 112 / 138

TCi Operator Manual
106
The estimated error contribution may be a few additional percentage points at temperatures
below 0

C and above 50

C.
9.7.5 Calibration
The TCi calibration curves are based on various sets of materials, which were tested for
conductivity and volumetric heat capacity by other methods and equipment. The measured
values of those materials are used for the TCi calibration curves. Since these values may have
accuracy errors of a few percentage points, these errors are naturally transferred to the TCi
sensor.
The overall accuracy of the TCi is estimated at 5% between 0

C and 50

C, and up to 10% above
or below that temperature range. The variation is typically 1-2% (%RSD calculated from at least
10 consecutive samples, at 0

C to 50

C).
The following mathematical analysis refers to variation in effusivity measurements, inflicted by
variation of the current between different measurements in any given set of measurements. The
analysis is limited to those cases where the calibration is linear, but intuitively it also applies to 2
nd
order effusivity equations.
It is assumed that the sensor and tested material are in equilibrium and at the same temperature
at the beginning of the set of measurements, and thus the sensor resistance,
R , is identical for all
measurements. It is further assumed that effusivities of sensor and measured material don’t
change during the measurement.
From (14)
2 1
1284 . 1
e e
G A I
m

 

we can write the variance in m as:
2 1
) ( 1284 . 1
e e
I G G I A
m

     
 
(32)
And the relative variance as:
I
I
G
G
G I
I G G I
e e
G A I
e e
I G G I A
m
m





    


 

     


2 1
2 1
1284 . 1
) ( 1284 . 1
(33)
Since G is proportional to I
2
( R is assumed constant from one measurement to another):
I
I
m
m



3
(34)
The relative variance in slope m ideally is triple the relative variance in current I . Intuitively this is
understood, since a stable current source will provide stable voltage measurements.
Note: equation (34) ignores second order errors.
It is generally known that: